The mechanical behavior of conductance arteries is viscoelastic. While the elastic component has been extensively studied, the viscous component has often been neglected for methodological reasons and also because it was considered weak. Unlike a purely elastic solid, which exhibits instantaneous deformation/relaxation upon application/discontinuation of a force, a viscoelastic solid is characterized, from a mechanical point of view, by a delay between the application or discontinuation of the force and deformation. Thus, at the arterial level, the elasticity of the arterial wall allows the internal diameter to increase proportionally to the blood pressure during systole. The viscous component will induce a delay in diameter restoration, resulting in a larger diameter at each pressure level during the diastolic phase compared to the systolic phase. This results in a shift between the systolic and diastolic curves of the pressure-diameter relationship, creating a hysteresis loop. From a thermodynamic point of view, while a purely elastic material fully restores the energy stored during the loading phase, viscoelastic arteries will incompletely restore this energy. Thus, the surface of the hysteresis loop reflects the energy dissipated during each cardiac cycle (WV), and the area under the loading phase curve represents the energy stored by the arterial wall (WE) during the latter. Thus, arterial wall viscosity (APV) can be expressed either as the absolute value of WV or as a function of the stored energy (WV/WE). Physiologically, this energy loss is low. Its increase could be accompanied by excessive energy dissipation, leading to increased cardiac work and cardio-circulatory decoupling. Conversely, low parietal viscosity could lead to damage to peripheral organs by excessive transmission of pulsatile energy to the periphery due to lack of damping.